Reasoning Determine Whether the Lines Will Be

¶ … Reasoning

Determine whether the lines will be perpendicular when graphed.

2x + 3y = 6

The slope of perpendicular lines are the negative reciprocal of one another, therefore will solve for the slope of each line. Slope can be determined by solving for m in the equation y= mx +b where m is the slope.

3x-2y=

3x-2y-3x= 6-3x

-2y= -3x +

y = 3x/2 -- 3

m= 3/2

2x + 3y = 6

2x = 6- 2x

3y= 6-2x

y = 2 -- 2x/3

m= -2/3

Because the slopes are negative reciprocals, the lines are perpendicular.

Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the number of seats in the smoking section. How many seats are in each section?

N= 73 + 2S

N+S = 205

+ 2S + S = 205

+ 3S =205

3S= 205-73

3S=132

S=

N= 73 + 2S

N= 73 + 2*

N= 73 +

N= 161

There are 44 seats in the smoking section and 161 seats in the non-smoking section.

Solve the system of equations by the substitution method

x + 3y = 32

-3x + 2y = 3

x + 3y = 32

x= 32-3y

-3x + 2y = 3

-3(32-3y) + 2y = 3

-96 + 9y + 2y = 3

-96 + 11y=3

11y= 96 + 3

11y= 99

y= 9

x = 32-3y

x= 32-(3*9)

x= 32-27

x=5

4. Solve the system of equations x + y = 5

x - y = -9

x + y = 5

x - y = -9

x= -9 + y x + y = 5

-9 + y + y = 5

-9 + 2y = 5

2y = 14

y=7

x-7 = -9

x= -9 + 7

x= -2